Demand response based on real time pricing introduces a new feedback loop between consumers' behavior and short term electricity markets. This feedback raises some concerns due to its potential destabilizing impact on electricity markets. Any analysis of this impact requires electricity market model. In this paper, several market models used for this purpose in the literature are analyzed and it is shown that the disagreement between the behavior of these models and reality is strong. For this reason an alternative model is proposed based on the structural approach to the electricity price modelling. This model is shown to be consistent with the real market data. It can be used to analyze the potential destabilizing impact of real time pricing in a more realistic way.